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-rw-r--r--core/math/math_2d.cpp105
-rw-r--r--core/math/math_2d.h96
2 files changed, 107 insertions, 94 deletions
diff --git a/core/math/math_2d.cpp b/core/math/math_2d.cpp
index 2ced18e427..df9383ed1b 100644
--- a/core/math/math_2d.cpp
+++ b/core/math/math_2d.cpp
@@ -31,22 +31,22 @@
real_t Vector2::angle() const {
- return Math::atan2(x,y);
+ return Math::atan2(y,x);
}
-float Vector2::length() const {
+real_t Vector2::length() const {
return Math::sqrt( x*x + y*y );
}
-float Vector2::length_squared() const {
+real_t Vector2::length_squared() const {
return x*x + y*y;
}
void Vector2::normalize() {
- float l = x*x + y*y;
+ real_t l = x*x + y*y;
if (l!=0) {
l=Math::sqrt(l);
@@ -62,32 +62,32 @@ Vector2 Vector2::normalized() const {
return v;
}
-float Vector2::distance_to(const Vector2& p_vector2) const {
+real_t Vector2::distance_to(const Vector2& p_vector2) const {
return Math::sqrt( (x-p_vector2.x)*(x-p_vector2.x) + (y-p_vector2.y)*(y-p_vector2.y));
}
-float Vector2::distance_squared_to(const Vector2& p_vector2) const {
+real_t Vector2::distance_squared_to(const Vector2& p_vector2) const {
return (x-p_vector2.x)*(x-p_vector2.x) + (y-p_vector2.y)*(y-p_vector2.y);
}
-float Vector2::angle_to(const Vector2& p_vector2) const {
+real_t Vector2::angle_to(const Vector2& p_vector2) const {
- return Math::atan2( tangent().dot(p_vector2), dot(p_vector2) );
+ return Math::atan2( cross(p_vector2), dot(p_vector2) );
}
-float Vector2::angle_to_point(const Vector2& p_vector2) const {
+real_t Vector2::angle_to_point(const Vector2& p_vector2) const {
- return Math::atan2( x-p_vector2.x, y - p_vector2.y );
+ return Math::atan2( y - p_vector2.y, x-p_vector2.x );
}
-float Vector2::dot(const Vector2& p_other) const {
+real_t Vector2::dot(const Vector2& p_other) const {
return x*p_other.x + y*p_other.y;
}
-float Vector2::cross(const Vector2& p_other) const {
+real_t Vector2::cross(const Vector2& p_other) const {
return x*p_other.y - y*p_other.x;
}
@@ -120,11 +120,11 @@ Vector2 Vector2::operator*(const Vector2 &p_v1) const {
return Vector2(x * p_v1.x, y * p_v1.y);
};
-Vector2 Vector2::operator*(const float &rvalue) const {
+Vector2 Vector2::operator*(const real_t &rvalue) const {
return Vector2(x * rvalue, y * rvalue);
};
-void Vector2::operator*=(const float &rvalue) {
+void Vector2::operator*=(const real_t &rvalue) {
x *= rvalue; y *= rvalue;
};
@@ -134,12 +134,12 @@ Vector2 Vector2::operator/(const Vector2 &p_v1) const {
return Vector2(x / p_v1.x, y / p_v1.y);
};
-Vector2 Vector2::operator/(const float &rvalue) const {
+Vector2 Vector2::operator/(const real_t &rvalue) const {
return Vector2(x / rvalue, y / rvalue);
};
-void Vector2::operator/=(const float &rvalue) {
+void Vector2::operator/=(const real_t &rvalue) {
x /= rvalue; y /= rvalue;
};
@@ -162,7 +162,7 @@ Vector2 Vector2::floor() const {
return Vector2( Math::floor(x), Math::floor(y) );
}
-Vector2 Vector2::rotated(float p_by) const {
+Vector2 Vector2::rotated(real_t p_by) const {
Vector2 v;
v.set_rotation(angle()+p_by);
@@ -198,7 +198,7 @@ Vector2 Vector2::clamped(real_t p_len) const {
return v;
}
-Vector2 Vector2::cubic_interpolate_soft(const Vector2& p_b,const Vector2& p_pre_a, const Vector2& p_post_b,float p_t) const {
+Vector2 Vector2::cubic_interpolate_soft(const Vector2& p_b,const Vector2& p_pre_a, const Vector2& p_post_b,real_t p_t) const {
#if 0
k[0] = ((*this) (vi[0] + 1, vi[1], vi[2])) - ((*this) (vi[0],
vi[1],vi[2])); //fk = a0
@@ -219,13 +219,13 @@ Vector2 Vector2::cubic_interpolate_soft(const Vector2& p_b,const Vector2& p_pre_
//dk = (fk+1 - fk-1)*0.5
//Dk = (fk+1 - fk)
- float dk =
+ real_t dk =
#endif
return Vector2();
}
-Vector2 Vector2::cubic_interpolate(const Vector2& p_b,const Vector2& p_pre_a, const Vector2& p_post_b,float p_t) const {
+Vector2 Vector2::cubic_interpolate(const Vector2& p_b,const Vector2& p_pre_a, const Vector2& p_post_b,real_t p_t) const {
@@ -234,9 +234,9 @@ Vector2 Vector2::cubic_interpolate(const Vector2& p_b,const Vector2& p_pre_a, co
Vector2 p2=p_b;
Vector2 p3=p_post_b;
- float t = p_t;
- float t2 = t * t;
- float t3 = t2 * t;
+ real_t t = p_t;
+ real_t t2 = t * t;
+ real_t t3 = t2 * t;
Vector2 out;
out = 0.5f * ( ( p1 * 2.0f) +
@@ -246,8 +246,8 @@ Vector2 Vector2::cubic_interpolate(const Vector2& p_b,const Vector2& p_pre_a, co
return out;
/*
- float mu = p_t;
- float mu2 = mu*mu;
+ real_t mu = p_t;
+ real_t mu2 = mu*mu;
Vector2 a0 = p_post_b - p_b - p_pre_a + *this;
Vector2 a1 = p_pre_a - *this - a0;
@@ -257,7 +257,7 @@ Vector2 Vector2::cubic_interpolate(const Vector2& p_b,const Vector2& p_pre_a, co
return ( a0*mu*mu2 + a1*mu2 + a2*mu + a3 );
*/
/*
- float t = p_t;
+ real_t t = p_t;
real_t t2 = t*t;
real_t t3 = t2*t;
@@ -291,7 +291,7 @@ bool Rect2::intersects_segment(const Point2& p_from, const Point2& p_to, Point2*
real_t min=0,max=1;
int axis=0;
- float sign=0;
+ real_t sign=0;
for(int i=0;i<2;i++) {
real_t seg_from=p_from[i];
@@ -299,7 +299,7 @@ bool Rect2::intersects_segment(const Point2& p_from, const Point2& p_to, Point2*
real_t box_begin=pos[i];
real_t box_end=box_begin+size[i];
real_t cmin,cmax;
- float csign;
+ real_t csign;
if (seg_from < seg_to) {
@@ -409,7 +409,8 @@ bool Point2i::operator!=(const Point2i& p_vec2) const {
}
void Matrix32::invert() {
-
+ // FIXME: this function assumes the basis is a rotation matrix, with no scaling.
+ // Matrix32::affine_inverse can handle matrices with scaling, so GDScript should eventually use that.
SWAP(elements[0][1],elements[1][0]);
elements[2] = basis_xform(-elements[2]);
}
@@ -424,9 +425,9 @@ Matrix32 Matrix32::inverse() const {
void Matrix32::affine_invert() {
- float det = basis_determinant();
+ real_t det = basis_determinant();
ERR_FAIL_COND(det==0);
- float idet = 1.0 / det;
+ real_t idet = 1.0 / det;
SWAP( elements[0][0],elements[1][1] );
elements[0]*=Vector2(idet,-idet);
@@ -444,14 +445,16 @@ Matrix32 Matrix32::affine_inverse() const {
}
void Matrix32::rotate(real_t p_phi) {
-
- Matrix32 rot(p_phi,Vector2());
- *this *= rot;
+ *this = Matrix32(p_phi,Vector2()) * (*this);
}
real_t Matrix32::get_rotation() const {
-
- return Math::atan2(elements[1].x,elements[1].y);
+ real_t det = basis_determinant();
+ Matrix32 m = orthonormalized();
+ if (det < 0) {
+ m.scale_basis(Size2(-1,-1));
+ }
+ return Math::atan2(m[0].y,m[0].x);
}
void Matrix32::set_rotation(real_t p_rot) {
@@ -459,9 +462,9 @@ void Matrix32::set_rotation(real_t p_rot) {
real_t cr = Math::cos(p_rot);
real_t sr = Math::sin(p_rot);
elements[0][0]=cr;
+ elements[0][1]=sr;
+ elements[1][0]=-sr;
elements[1][1]=cr;
- elements[0][1]=-sr;
- elements[1][0]=sr;
}
Matrix32::Matrix32(real_t p_rot, const Vector2& p_pos) {
@@ -469,27 +472,27 @@ Matrix32::Matrix32(real_t p_rot, const Vector2& p_pos) {
real_t cr = Math::cos(p_rot);
real_t sr = Math::sin(p_rot);
elements[0][0]=cr;
+ elements[0][1]=sr;
+ elements[1][0]=-sr;
elements[1][1]=cr;
- elements[0][1]=-sr;
- elements[1][0]=sr;
elements[2]=p_pos;
}
Size2 Matrix32::get_scale() const {
-
- return Size2( elements[0].length(), elements[1].length() );
+ real_t det_sign = basis_determinant() > 0 ? 1 : -1;
+ return det_sign * Size2( elements[0].length(), elements[1].length() );
}
void Matrix32::scale(const Size2& p_scale) {
-
- elements[0]*=p_scale;
- elements[1]*=p_scale;
+ scale_basis(p_scale);
elements[2]*=p_scale;
}
void Matrix32::scale_basis(const Size2& p_scale) {
- elements[0]*=p_scale;
- elements[1]*=p_scale;
+ elements[0][0]*=p_scale.x;
+ elements[0][1]*=p_scale.y;
+ elements[1][0]*=p_scale.x;
+ elements[1][1]*=p_scale.y;
}
void Matrix32::translate( real_t p_tx, real_t p_ty) {
@@ -548,7 +551,7 @@ void Matrix32::operator*=(const Matrix32& p_transform) {
elements[2] = xform(p_transform.elements[2]);
- float x0,x1,y0,y1;
+ real_t x0,x1,y0,y1;
x0 = tdotx(p_transform.elements[0]);
x1 = tdoty(p_transform.elements[0]);
@@ -601,7 +604,7 @@ Matrix32 Matrix32::translated(const Vector2& p_offset) const {
}
-Matrix32 Matrix32::rotated(float p_phi) const {
+Matrix32 Matrix32::rotated(real_t p_phi) const {
Matrix32 copy=*this;
copy.rotate(p_phi);
@@ -609,12 +612,12 @@ Matrix32 Matrix32::rotated(float p_phi) const {
}
-float Matrix32::basis_determinant() const {
+real_t Matrix32::basis_determinant() const {
return elements[0].x * elements[1].y - elements[0].y * elements[1].x;
}
-Matrix32 Matrix32::interpolate_with(const Matrix32& p_transform, float p_c) const {
+Matrix32 Matrix32::interpolate_with(const Matrix32& p_transform, real_t p_c) const {
//extract parameters
Vector2 p1 = get_origin();
diff --git a/core/math/math_2d.h b/core/math/math_2d.h
index 2ec0dc39c5..adc23f01b1 100644
--- a/core/math/math_2d.h
+++ b/core/math/math_2d.h
@@ -65,35 +65,35 @@ enum VAlign {
struct Vector2 {
union {
- float x;
- float width;
+ real_t x;
+ real_t width;
};
union {
- float y;
- float height;
+ real_t y;
+ real_t height;
};
- _FORCE_INLINE_ float& operator[](int p_idx) {
+ _FORCE_INLINE_ real_t& operator[](int p_idx) {
return p_idx?y:x;
}
- _FORCE_INLINE_ const float& operator[](int p_idx) const {
+ _FORCE_INLINE_ const real_t& operator[](int p_idx) const {
return p_idx?y:x;
}
void normalize();
Vector2 normalized() const;
- float length() const;
- float length_squared() const;
+ real_t length() const;
+ real_t length_squared() const;
- float distance_to(const Vector2& p_vector2) const;
- float distance_squared_to(const Vector2& p_vector2) const;
- float angle_to(const Vector2& p_vector2) const;
- float angle_to_point(const Vector2& p_vector2) const;
+ real_t distance_to(const Vector2& p_vector2) const;
+ real_t distance_squared_to(const Vector2& p_vector2) const;
+ real_t angle_to(const Vector2& p_vector2) const;
+ real_t angle_to_point(const Vector2& p_vector2) const;
- float dot(const Vector2& p_other) const;
- float cross(const Vector2& p_other) const;
+ real_t dot(const Vector2& p_other) const;
+ real_t cross(const Vector2& p_other) const;
Vector2 cross(real_t p_other) const;
Vector2 project(const Vector2& p_vec) const;
@@ -101,10 +101,10 @@ struct Vector2 {
Vector2 clamped(real_t p_len) const;
- _FORCE_INLINE_ static Vector2 linear_interpolate(const Vector2& p_a, const Vector2& p_b,float p_t);
- _FORCE_INLINE_ Vector2 linear_interpolate(const Vector2& p_b,float p_t) const;
- Vector2 cubic_interpolate(const Vector2& p_b,const Vector2& p_pre_a, const Vector2& p_post_b,float p_t) const;
- Vector2 cubic_interpolate_soft(const Vector2& p_b,const Vector2& p_pre_a, const Vector2& p_post_b,float p_t) const;
+ _FORCE_INLINE_ static Vector2 linear_interpolate(const Vector2& p_a, const Vector2& p_b,real_t p_t);
+ _FORCE_INLINE_ Vector2 linear_interpolate(const Vector2& p_b,real_t p_t) const;
+ Vector2 cubic_interpolate(const Vector2& p_b,const Vector2& p_pre_a, const Vector2& p_post_b,real_t p_t) const;
+ Vector2 cubic_interpolate_soft(const Vector2& p_b,const Vector2& p_pre_a, const Vector2& p_post_b,real_t p_t) const;
Vector2 slide(const Vector2& p_vec) const;
Vector2 reflect(const Vector2& p_vec) const;
@@ -115,15 +115,15 @@ struct Vector2 {
void operator-=(const Vector2& p_v);
Vector2 operator*(const Vector2 &p_v1) const;
- Vector2 operator*(const float &rvalue) const;
- void operator*=(const float &rvalue);
+ Vector2 operator*(const real_t &rvalue) const;
+ void operator*=(const real_t &rvalue);
void operator*=(const Vector2 &rvalue) { *this = *this * rvalue; }
Vector2 operator/(const Vector2 &p_v1) const;
- Vector2 operator/(const float &rvalue) const;
+ Vector2 operator/(const real_t &rvalue) const;
- void operator/=(const float &rvalue);
+ void operator/=(const real_t &rvalue);
Vector2 operator-() const;
@@ -135,10 +135,10 @@ struct Vector2 {
real_t angle() const;
- void set_rotation(float p_radians) {
+ void set_rotation(real_t p_radians) {
- x=Math::sin(p_radians);
- y=Math::cos(p_radians);
+ x=Math::cos(p_radians);
+ y=Math::sin(p_radians);
}
_FORCE_INLINE_ Vector2 abs() const {
@@ -146,7 +146,7 @@ struct Vector2 {
return Vector2( Math::abs(x), Math::abs(y) );
}
- Vector2 rotated(float p_by) const;
+ Vector2 rotated(real_t p_by) const;
Vector2 tangent() const {
return Vector2(y,-x);
@@ -154,12 +154,12 @@ struct Vector2 {
Vector2 floor() const;
Vector2 snapped(const Vector2& p_by) const;
- float get_aspect() const { return width/height; }
+ real_t get_aspect() const { return width/height; }
operator String() const { return String::num(x)+", "+String::num(y); }
- _FORCE_INLINE_ Vector2(float p_x,float p_y) { x=p_x; y=p_y; }
+ _FORCE_INLINE_ Vector2(real_t p_x,real_t p_y) { x=p_x; y=p_y; }
_FORCE_INLINE_ Vector2() { x=0; y=0; }
};
@@ -169,12 +169,12 @@ _FORCE_INLINE_ Vector2 Vector2::plane_project(real_t p_d, const Vector2& p_vec)
}
-_FORCE_INLINE_ Vector2 operator*(float p_scalar, const Vector2& p_vec) {
+_FORCE_INLINE_ Vector2 operator*(real_t p_scalar, const Vector2& p_vec) {
return p_vec*p_scalar;
}
-Vector2 Vector2::linear_interpolate(const Vector2& p_b,float p_t) const {
+Vector2 Vector2::linear_interpolate(const Vector2& p_b,real_t p_t) const {
Vector2 res=*this;
@@ -185,7 +185,7 @@ Vector2 Vector2::linear_interpolate(const Vector2& p_b,float p_t) const {
}
-Vector2 Vector2::linear_interpolate(const Vector2& p_a, const Vector2& p_b,float p_t) {
+Vector2 Vector2::linear_interpolate(const Vector2& p_a, const Vector2& p_b,real_t p_t) {
Vector2 res=p_a;
@@ -211,7 +211,7 @@ struct Rect2 {
const Vector2& get_size() const { return size; }
void set_size(const Vector2& p_size) { size=p_size; }
- float get_area() const { return size.width*size.height; }
+ real_t get_area() const { return size.width*size.height; }
inline bool intersects(const Rect2& p_rect) const {
if ( pos.x >= (p_rect.pos.x + p_rect.size.width) )
@@ -226,9 +226,9 @@ struct Rect2 {
return true;
}
- inline float distance_to(const Vector2& p_point) const {
+ inline real_t distance_to(const Vector2& p_point) const {
- float dist = 1e20;
+ real_t dist = 1e20;
if (p_point.x < pos.x) {
dist=MIN(dist,pos.x-p_point.x);
@@ -359,7 +359,7 @@ struct Rect2 {
operator String() const { return String(pos)+", "+String(size); }
Rect2() {}
- Rect2( float p_x, float p_y, float p_width, float p_height) { pos=Point2(p_x,p_y); size=Size2( p_width, p_height ); }
+ Rect2( real_t p_x, real_t p_y, real_t p_width, real_t p_height) { pos=Point2(p_x,p_y); size=Size2( p_width, p_height ); }
Rect2( const Point2& p_pos, const Size2& p_size ) { pos=p_pos; size=p_size; }
};
@@ -407,7 +407,7 @@ struct Point2i {
bool operator==(const Point2i& p_vec2) const;
bool operator!=(const Point2i& p_vec2) const;
- float get_aspect() const { return width/(float)height; }
+ real_t get_aspect() const { return width/(real_t)height; }
operator String() const { return String::num(x)+", "+String::num(y); }
@@ -552,11 +552,21 @@ struct Rect2i {
struct Matrix32 {
+ // Warning #1: basis of Matrix32 is stored differently from Matrix3. In terms of elements array, the basis matrix looks like "on paper":
+ // M = (elements[0][0] elements[1][0])
+ // (elements[0][1] elements[1][1])
+ // This is such that the columns, which can be interpreted as basis vectors of the coordinate system "painted" on the object, can be accessed as elements[i].
+ // Note that this is the opposite of the indices in mathematical texts, meaning: $M_{12}$ in a math book corresponds to elements[1][0] here.
+ // This requires additional care when working with explicit indices.
+ // See https://en.wikipedia.org/wiki/Row-_and_column-major_order for further reading.
+
+ // Warning #2: 2D be aware that unlike 3D code, 2D code uses a left-handed coordinate system: Y-axis points down,
+ // and angle is measure from +X to +Y in a clockwise-fashion.
Vector2 elements[3];
- _FORCE_INLINE_ float tdotx(const Vector2& v) const { return elements[0][0] * v.x + elements[1][0] * v.y; }
- _FORCE_INLINE_ float tdoty(const Vector2& v) const { return elements[0][1] * v.x + elements[1][1] * v.y; }
+ _FORCE_INLINE_ real_t tdotx(const Vector2& v) const { return elements[0][0] * v.x + elements[1][0] * v.y; }
+ _FORCE_INLINE_ real_t tdoty(const Vector2& v) const { return elements[0][1] * v.x + elements[1][1] * v.y; }
const Vector2& operator[](int p_idx) const { return elements[p_idx]; }
Vector2& operator[](int p_idx) { return elements[p_idx]; }
@@ -580,7 +590,7 @@ struct Matrix32 {
void translate( real_t p_tx, real_t p_ty);
void translate( const Vector2& p_translation );
- float basis_determinant() const;
+ real_t basis_determinant() const;
Size2 get_scale() const;
@@ -590,7 +600,7 @@ struct Matrix32 {
Matrix32 scaled(const Size2& p_scale) const;
Matrix32 basis_scaled(const Size2& p_scale) const;
Matrix32 translated(const Vector2& p_offset) const;
- Matrix32 rotated(float p_phi) const;
+ Matrix32 rotated(real_t p_phi) const;
Matrix32 untranslated() const;
@@ -603,7 +613,7 @@ struct Matrix32 {
void operator*=(const Matrix32& p_transform);
Matrix32 operator*(const Matrix32& p_transform) const;
- Matrix32 interpolate_with(const Matrix32& p_transform, float p_c) const;
+ Matrix32 interpolate_with(const Matrix32& p_transform, real_t p_c) const;
_FORCE_INLINE_ Vector2 basis_xform(const Vector2& p_vec) const;
_FORCE_INLINE_ Vector2 basis_xform_inv(const Vector2& p_vec) const;
@@ -834,8 +844,8 @@ void Matrix32::set_rotation_and_scale(real_t p_rot,const Size2& p_scale) {
elements[0][0]=Math::cos(p_rot)*p_scale.x;
elements[1][1]=Math::cos(p_rot)*p_scale.y;
- elements[0][1]=-Math::sin(p_rot)*p_scale.x;
- elements[1][0]=Math::sin(p_rot)*p_scale.y;
+ elements[1][0]=-Math::sin(p_rot)*p_scale.y;
+ elements[0][1]=Math::sin(p_rot)*p_scale.x;
}
generated by cgit v1.2.3 (git 2.25.1) at 2025-02-17 04:45:46 +0000